Chemistry Reference
In-Depth Information
uniform. He also assumed that the angular frequency of the weak field is close to
the Larmor frequency of the system
ω
0
=
γH
0
(36)
Therefore, the
x
-direction field can be replaced by a field that rotates about the
z
-axis,
H
x
=
H
1
cos
ωt
H
y
=±
H
1
sin
ωt
z
is the direction of rotation as signified by the sign of the
y
-component. Bloch
introduced a polar angle,
θ
, which has a constant value such that,
γH
1
γH
0
±
tan
θ
=
(37)
ω
Next, by letting
ω
|
H
∗
|
=
(38)
γ
where
H
∗
denotes the field at which the Larmor frequency is equal to the frequency
of
H
1
, such that,
H
1
H
0
−
tan
θ
=
(39)
H
∗
and writing
M
x
=
M
sin
θ
cos
ωt
M
y
=±
M
sin
θ
sin
ωt
M
z
=
M
cos
θ
(40)
It is clear that
M
, the magnitude of the magnetization, is constant. Equation (40)
demonstrates that the magnetization rotates about the
z
-axis, in the plane common
to the rotating
x
-
y
and the
z
-component. By introducing,
H
∗
H
0
−
δ
=
=
cot
θ
(41)
H
1
where
δ
is the deviation between the static field
H
0
, and the resonance value of
this field
H
∗
normalized with respect to the magnitude of the oscillating field
H
1
.
